The Saudis and Iranians don’t agree on much, but they do share a deep dislike for Muammer Gaddafi. In fact, outside of Venezuela’s President Hugo Chávez, there really is no one in the international community who does. That is why it was so easy to build international support for a Nato bid to push him from power.

The trouble is that, unless it gets exceptionally lucky, Nato is unlikely to either force Col Gaddafi from his stronghold or cut a politically saleable deal with him anytime soon. Meanwhile, the opposition are making little progress, a fact now worsened by the death of their military leader, Abdel Fattah Younis, who defected from Col Gaddafi in February. The most likely outcome remains a country in pieces, with substantial volumes of crude oil offline for at least the new few months.

This now creates considerable risk for the western governments implicated in the efforts to oust him. The ease with which Nato entered this fight has in turn made it easier to become more deeply enmeshed in it. Few strenuously objected when the mission began to creep, and now it seems that nothing short of Col Gaddafi’s departure, on a plane or in a coffin, can can truly bring this conflict to an end.

This is an especially bad situation for President Barack Obama, a man most comfortable steering conflict toward compromise. Though Britain and France now say that Col Gaddafi can remain in Libya as long as he relinquishes power, there appears to be no true middle ground to allow this compromise to come about.

In power since The Beatles were cutting new albums, Col Gaddafi has made clear that he won’t retire, particularly since the International Criminal Court has issued a warrant for his arrest. He already lives with the risk that the next whistling noise in the skies above might be the last sound he hears.

Nor are Libya’s rebels likely to allow his children to inherit his power, or to create a government of their own with their father living happily in a tent in Libya’s desert, lobbing threats in their direction. Nor is Col Gaddafi likely to be willing to live inside Libya with less than total political control: he knows that when a new government comes to arrest him, no one will object.

As Robert Gates made plain in his final address as US defence secretary to Nato members, Europe’s commitment to funding this adventure is also on the wane – though it was the Europeans who initially led this charge – and American lawmakers, now playing chicken with their country’s credit rating, are in no mood to pick up another cheque.

So the transatlantic military alliance now faces two unsavoury choices. It can put the proverbial “boots on the ground” to oust Col Gaddafi, and bring the military chapter of this mission to a definitive close. That would satisfy some, but enrage many others. Or they can cut a deal that leaves the rebels where they are with Gaddafi as mayor of Tripoli. This de facto partition plan would frustrate virtually everyone. Understandably, no one is prepared to make this choice.

And so the stalemate will continue. Nato must now hope it gets lucky. In the mean time, its participants should reflect on the moral of this story for those western powers anxious to write its final chapter: a lack of international resistance can lead governments to start wars they don’t know how to win.

The writer is the president of Eurasia Group, a political risk consultancy, and author of ‘The End of the Free Market’